Potential energy

Introduction

All objects have energy. The word energy comes from the Greek word energeia ( $έ\nu έ\rho \gamma \epsilon \iota \alpha$ ), meaning activity or operation. Energy is closely linked to mass and cannot be created or destroyed. In this chapter we will consider potential and kinetic energy.

Potential energy

The potential energy of an object is generally defined as the energy an object has because of its position relative to other objects that it interacts with. There are different kinds of potential energy such as gravitional potential energy, chemical potential energy, electrical potential energy, to name a few. In this section we will be looking at gravitational potential energy.

Potential energy

Potential energy is the energy an object has due to its position or state.

Gravitational potential energy is the energy of an object due to its position above the surface of the Earth. The symbol $E_P$ is used to refer to gravitational potential energy. You will often find that the words potential energy are used where gravitational potential energy is meant. We can define potential energy (or gravitational potential energy, if you like) as:

where $E_P$ = potential energy measured in joules (J)

m = mass of the object (measured in kg)

g = gravitational acceleration ( $\mathrm{9,8}\mathrm{m}·\mathrm{s}{}^{-2}$ )

h = perpendicular height from the reference point (measured in m)

A suitcase, with a mass of $1\mathrm{kg}$ , is placed at the top of a $2\mathrm{m}$ high cupboard. By lifting the suitcase against the force of gravity, we give the suitcase potential energy. This potential energy can be calculated using [link] .

If the suitcase falls off the cupboard, it will lose its potential energy. Halfway down the cupboard, the suitcase will have lost half its potential energy and will have only $\mathrm{9,8}\mathrm{J}$ left. At the bottom of the cupboard the suitcase will have lost all it's potential energy and it's potential energy will be equal to zero.

Objects have maximum potential energy at a maximum height and will lose their potential energy as they fall.

Gravitational potential energy

1. Describe the relationship between an object's gravitational potential energy and its:
   1. mass and
   2. height above a reference point.
2. A boy, of mass $30\mathrm{kg}$ , climbs onto the roof of a garage. The roof is $\mathrm{2,5}\mathrm{m}$ from the ground. He now jumps off the roof and lands on the ground.
   1. How much potential energy has the boy gained by climbing on the roof?
   2. The boy now jumps down. What is the potential energy of the boy when he is $1m$ from the ground?
   3. What is the potential energy of the boy when he lands on the ground?
3. A hiker walks up a mountain, $800\mathrm{m}$ above sea level, to spend the night at the top in the first overnight hut. The second day he walks to the second overnight hut, $500\mathrm{m}$ above sea level. The third day he returns to his starting point, $200\mathrm{m}$ above sea level.
   1. What is the potential energy of the hiker at the first hut (relative to sea level)?
   2. How much potential energy has the hiker lost during the second day?
   3. How much potential energy did the hiker have when he started his journey (relative to sea level)?
   4. How much potential energy did the hiker have at the end of his journey?